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Gaussian Process Models for Visualisation of High Dimensional Data
Advances in Neural Information Processing Systems, MIT Press 16:329-336, 2004.
Abstract
In this paper we introduce a new underlying probabilistic model for
principal component analysis (PCA). Our formulation interprets PCA
as a particular Gaussian process prior on a mapping from a latent
space to the observed data-space. We show that if the prior's
covariance function constrains the mappings to be linear the model
is equivalent to PCA, we then extend the model by considering less
restrictive covariance functions which allow non-linear
mappings. This more general Gaussian process latent variable model
(GPLVM) is then evaluated as an approach to the visualisation of
high dimensional data for three different data-sets. Additionally
our non-linear algorithm can be *further* kernelised leading to
'twin kernel PCA' in which a *mapping between feature spaces*
occurs.